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Introduction to Exponents
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Remember, multiplication is the shortcut for doing repeated addition:
$$6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 54$$
$$6 \times 9 = 54$$

Similarly, there is a shortcut to writing multiplication if you do the same thing over and over again:
$$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 128$$

Here we multiplied 2 together 7 times.

For the shorthand, we write $$2^7 = 128$$

That little 7 means the number of times that we multiply 2 by itself and is called an exponent; sometimes we call it a power.

Here are a couple more examples:

$$5^3 = 5 \times 5 \times 5=125$$
$$7^2 = 7 \times 7 = 49$$
$$2^4 = 2 \times 2 \times 2 \times 2 = 16$$

Some of the easiest to calculate are the powers of 10. Try these:

$$10^2 = 100$$
$$10^4 = 10,000$$
$$10^8 = 100,000,000$$

Notice a pattern?

### Scripture Connection

Alma 37:6

Like the small and simple things in this scripture, exponents also bring about great things. They are tiny numbers that make a big difference on the outcome of the answer.

Introduction to Exponents
Evaluating numbers with exponents

### Practice Problems

Evaluate the following expression:
1. $$1^2\, = \,?$$ (
Solution
Solution: 1
Details: Anytime 1 is used in multiplication, the answer is the other factor (numbers used in a multiplication problem). In this example $$1^2 = 1 \times 1 = 1$$
)
2. $$8^2\, = \,?$$ (
Video Solution
Solution: 64
Details:

(Video Source | Transcript)
)
3. $$0^3\, = \,?$$ (
Solution
Solution: 0
Details:
As we’ve seen in multiplication, any number multiplied by zero is 0:
$$0^3 = 0 × 0 × 0 = 0$$
)
4. $$5^3\, = \,?$$ (
Solution
Solution: 125
Details:
$$5^{3}$$ means 5 is being multiplied to itself 3 times.

$$5 \times 5 \times 5$$

Since everything is being multiplied together, we can start on the left and move right, doing one operation at a time.

$$(5 \times 5) \times 5 =$$

$$25 \times 5 =$$

)
5. $$4^3\, = \,?$$ (
Video Solution
Solution: 64
Details:

(Video Source | Transcript)
)
6. $$3^4\, = \,?$$ (
Solution
Solution:
81
)

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